Electronic Supplement to
Slow Fourier Transform

doi: 10.1785/0220120139

by Klaus-G. Hinzen, Sharon K. Reamer, and Frank Scherbaum


A fully interactive numerical model of the MOHA has been implemented in the open Computable Document Format (CDF), described at http://www.wolfram.com/cdf/. It illustrates the determination of the Fourier series coefficients a1 –a10 and b1 – b10 for a set of selected time series. It can operate in two modes of operation. In the Freehand mode, the user controls the tracepoint P with the mouse. Once the end of the trace is reach, the tracepoint can be automatically moved back to the origin by first moving vertically to the zero line and then back to the origin by hitting the Automatic Finish button. This way, the tracking error is purely related to the imprecision of the user to follow the actual trace and not from closing the loop to the origin. In the Autotracking mode, the actual tracking error is further reduced to the numerical and sampling error because the user moves the trace point with a slider along the time series and back to the origin. This mode is particularly instructive for the illustration of the working principle of the Mader-Ott mechanical harmonic analyzer. Simultaneous with the movement of the tracepoint, the simulated planimeter (the framed yellow rectangle attached to the planimeter pivot point), displays the momentary area within the trace of the selected cogwheel pin. The cogwheel pins and the corresponding pin traces are colored red and blue for the b- and a- coefficients, respectively.

CDF File

Download/View: MaderOtt.cdf [CDF file; 1.6 MB].

Note: Requires Wolfram CDF Player™ software, available as a free download from http://www.wolfram.com/cdf-player/
(currently available for Microsoft Windows, Mac OS X, and Linux).
If this software is already installed on your computer the linked file may load in your web browser window using the included CDF Player browser plug-in rather than downloading.

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